Distributive Property

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ISEE Lower Level Quantitative Reasoning › Distributive Property

Questions 1 - 10
1

Use the distributive property to find an equivalent expression.

Explanation

The distributive property is needed to solve this problem. The distributive property is . In this particular, case the FOIL technique should be used to expand this expression. FOIL is an acronym that helps students remember to multiply the first terms in each parentheses, then the outside terms in each parentheses, followed by multiplying the inside terms and then finally multiplying the last terms in each parentheses.





The final step is to combine like terms. Thus, the correct answer is:

2

Use the distributive property to solve for .

Explanation

The distributive property needs to be used to solve this expression for x.

The distributive property is:


From here we need to subtract 48 from both sides to isolate -6x.

Now we need to divide by -6 in order to solve for x.

3

Use the distributive property to expand the expression:

Explanation

The distributive property is needed to solve this problem. The distributive property is . In this particular, case the FOIL technique should be used to expand this expression. FOIL is an acronym that helps students remember to multiply the first terms in each parentheses, then the outside terms in each parentheses, followed by multiplying the inside terms and then finally multiplying the last terms in each parentheses.





The final step to expand this expression is to combine like terms. Thus, the correct answer is

4

Use the distributive property to find an equivalent expression.

Explanation

The distributive property is needed to solve this problem. The distributive property is . In this particular, case the FOIL technique should be used to expand this expression. FOIL is an acronym that helps students remember to multiply the first terms in each parentheses, then the outside terms in each parentheses, followed by multiplying the inside terms and then finally multiplying the last terms in each parentheses.





The final step is to combine like terms. Thus, the correct answer is:

5

Use the distributive property to solve for .

Explanation

The distributive property needs to be used to solve this expression for x.

The distributive property is:


From here we need to subtract 48 from both sides to isolate -6x.

Now we need to divide by -6 in order to solve for x.

6

Use the distributive property to expand the expression:

Explanation

The distributive property is needed to solve this problem. The distributive property is . In this particular, case the FOIL technique should be used to expand this expression. FOIL is an acronym that helps students remember to multiply the first terms in each parentheses, then the outside terms in each parentheses, followed by multiplying the inside terms and then finally multiplying the last terms in each parentheses.





The final step to expand this expression is to combine like terms. Thus, the correct answer is

7

Sharon purchased pieces of candy and wants to make Halloween treat bags for the children in her neighborhood. How many different ways can Sharon make treat bags with an even number of pieces of candy in each bag?

Explanation

We will solve this problem by finding factor pairs. Factor pairs are composed of two numbers that are multiplied together to equal a product. List all the factor pairs of Sharon’s candy.

Do not forget to list their reciprocals.

Sharon can make different treat bag combinations with an even amount of candy in each bag.

8

Sam purchased gummy bears and wants to make gift bags to give to his friends at school. How many different ways can Sam make gift bags with an even number of gummy bears in each bag?

Explanation

We will solve this problem by finding factor pairs. Factor pairs are composed of two numbers that are multiplied together to equal a product. List all the factor pairs of Sam’s gummy bears.

Do not forget to list their reciprocals.

Sam can make different gift bag combinations with an even amount of gummy bears in each bag.

9

Sam purchased gummy bears and wants to make gift bags to give to his friends at school. How many different ways can Sam make gift bags with an even number of gummy bears in each bag?

Explanation

We will solve this problem by finding factor pairs. Factor pairs are composed of two numbers that are multiplied together to equal a product. List all the factor pairs of Sam’s gummy bears.

Do not forget to list their reciprocals.

Sam can make different gift bag combinations with an even amount of gummy bears in each bag.

10

Simplify the following using the distributive property.

Explanation

To solve using the distributive property, we take the number on the outside and multiply it by each term on the inside of the parentheses.

So in the problem,

we will multiply or distribute the 5 through.

We will multiply the 5 by the first term. We get

Now, we multiply the 5 by the second term. We get

Now, we combine the two answers. We get

or

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